Typo
Currently, the solution says "We test that the derivative at a point in the interval, say x = 1 / 2, which gives a value of 6\cdot 2^{7/5}/5(-1/2) < 0 . Thus the function is increasing on this interval."
This should say "decreasing" since it is <0.
Just to clarify any confusion :)
So overall, the function is increasing on (-infinity; 0)U(1, infinity) and decreasing on (0, 1).